Mr. J Gallagher
Algebra - Worksheet
Junior Cert - Ordinary Level
Add and subtract the like terms
Simplify the following expressions
a) 16a – 4c + 10b + 6a – 7b + 3c
b) -14x + 11y + 4x – 13y
Evaluating Expressions
Evaluate the following expressions when x = 2, y = -3
a) x2 – 4xy
b) 6xy + 3x2y
c) x2 – y2
Multiplying Brackets
Simplify the following expressions
a) 4(3x - 4) + 3(-2x + 5)
b) -3(2x – 6y) – 4(x – y)
c) 7(2a + 3b) +6(4a – 2b) - 4(3b – 2a)
d) (3x - 4) (-2x + 5)
Simplifying Fractions
Simplify the following expression
a)
b)
c)
d)
𝑥+3
2
−
2𝑥−1
3
𝑥−2
5
3
𝑥+3
5
2
+
+
8𝑥−3
2𝑥+4
−
3𝑥−2
2𝑥−1
4
3
𝑥−3
+
, hence solve
4
, hence solve
, hence solve
𝑥−2
5
+
5
3𝑥−2
4
𝑥−3
4𝑥−2
8𝑥−3
5
3
, hence solve
+
2𝑥+4
4
+
=
=2
11
10
4𝑥−2
5
=1
= 5
Mr. J Gallagher
Factorising
Common Factors - Factorise the following expressions
a) x2 + 2x
b) 2y2 + 4y
c) 4xy – 12x2
d) 3x2y – 15xy
Difference of two squares - Factorise the following expressions
a) x2 – 49
b) y2 – 144
c) 4x2 – 25
d) 36y2 – 16x2
Grouping factors - Factorise the following expressions
a) ax + ay + bx + by
b) 3ax – 2ay + 3bx – 2by
c) 4x – 4y + abx – aby
Factorising quadratics - Factorise the following expressions
a) x2 – x – 20
b) x2 + 3x – 10
c) 4x2 + 4x + 1
d) 14x2 + 3x – 2
Quadratic equations - Solve the following equations
a) x2 – x – 20 = 0
b) x2 + 3x – 10 = 0
c) 4x2 + 4x + 1 = 0
d) 14x2 + 3x – 2 = 0
Mr. J Gallagher
Linear Equations
Solve the following equations
a) x + 2 = 0
b) 4x + 3 = 15
c) 3y – 6 = 18
d) 3x – 1 = 2x + 11
Linear equations with brackets - Solve the following equations
a) 3(x + 2) = 0
b) -3(4x + 3) = 15
c) 3(2y – 6) = 18
d) 4(x – 2) = 3(2x + 4)
e) 3(x – 2) = 7(x + 5) – 13
f) 2(2x + 1) – 3 (x – 1) = 9
Simultaneous Equations
Linear Simultaneous Equations – Solve the following for x & y
a) x – y = 1
2x + y = 11
b) 3x + 2y = 8
2x – 2y = 2
c) 2x + 3y = 8
5x + 3y = 11
d) 4x + y = -2
3x + y = -1
Inequalities
Linear – Solve the following inequality and graph your solution on a number line
a) 2x – 3 ≤ 5,
x𝜖R
b) 3x – 1 > 8,
x𝜖N
c) 4x + 3 < 3x + 10,
x𝜖R
d) 6(x + 4) > 2(x – 3)
x𝜖R
Mr. J Gallagher
Evaluating Functions
If the function f(x) = 5x – 2, find
a) f(-1)
b) f(3)
c) f(x) = 3
If the function f(x) = x2 – 6, find
a) f(-1)
b) f(3)
c) f(x) = 3
Graphing Functions
Graph the following linear functions
a) f: x  2x + 1 in the domain, -3 ≤ x ≤ 3.

Find the value when f(x) = 0

Find the value when x = 2.5
b) f: x  3x – 2 in the domain, -2 ≤ x ≤ 4.
Find the value when f(x) = 0
Find the value when x = 2.5
Graph the following quadratic functions
a) f: x  x2 – 4x – 5 in the domain, -3 ≤ x ≤ 3.
Find the values when f(x) = 0
Find the value when x = 2.5
b) f: x  2x2 + 4 in the domain, -3 ≤ x ≤ 3.
Find the values when f(x) = 0
Find the value when x = 2.5
Mr. J Gallagher
Real Life Examples
1. Brendan thinks of a number, adds three and the answer is fifteen. Represent
this statement as an equation. Solve the equation and check your answer.
2. Ryan thinks of a number then subtracts five and the answer is ten. Represent
this statement as an equation. Solve the equation and then check your answer.
3. A farmer has a number of cows and he plans to double that number next year,
when he will have twenty-four. Represent this statement as an equation. Solve
the equation and check your answer.
4. A new student enters class and the class now has twenty-five students.
Represent this statement as an equation. Solve the equation and check your
answer.
5. The temperature increases by eighteen degrees and the temperature is now
fifteen degrees. Represent this statement as an equation. Solve the equation
and check your answer.
6. A farmer doubles the amount of cows he has and then buys a further three
cows. He now has twenty-nine. Represent this statement as an equation. How
many did he originally have?
7. Emma and her twin brother will have a total age of forty-two in five years
time. Represent this statement as an equation. How old are they at the
moment?
8. Mark had some cookies. He gave half of them to his friend John. He then
divided his remaining cookies evenly between his other three friends each of
whom got four cookies. How many had he originally?